If pivot points (as defined in here) are just a matter of the law of the lever, don't you have to take into account that mass distribution isn't homogeneous in swords? I assume that the model gets far more complex if you include that every (infinite small) cross section segment has its own weight (due to taper e.g.).

Ah but it is taken into account... I don't really think of pivot points in terms of lever, but in terms of inertia, and inertia takes the variation of mass distribution into account, that's the whole point.

Think of it as successive approximations. Let's say that you divide, as you said, your weapon in many small segments, each with its own position x and mass m. I don't know if it's really an accepted terminology in english, but you could speak of:

* Zero-order moment: the sum of all m for all your little segments (I'll note that as sum(m)). This is obviously the mass of the weapon, M... Gives you an idea of how much matter there is but nothing else.
* First-order moment: sum(m * x). I'm noting the multiplication by a star to clarify. Divide that by M and you get the position of the center of gravity g... This is the average location of the mass. Now you know where the mass is on average, but it could be a single mass, two masses a bit aapart a stick, whatever... But your idea is more precise already.

Right, both of those quantity are routinely measured. But you can go on:

* Second-order moment: sum(m * (x-g)²)=sum(m * (x-g) * (x-g)). This is the inertia. This is what gives you the pivot points. It represents how far on average the mass is from the center of gravity. Now you have an idea of the extension of the mass in space. You still don't know what shape it has exactly, but the idea is still more precise...

As far as dynamics are concerned, we can stop here. The laws of motion (admitting that Newton is right, but it seems to work pretty decently if you're not building a spaceship ) allow to show that for any given solid object, those are the only three quantities that matter. Well in the most general case it would be more complicated, because the inertia is represented by 6 numbers arranged in a 3x3 matrix, but for object that are largely line-like, like most weapons, it's a very good approximation.

Of course you could go on with third-, fourth-order moment, and so on... But this won't add anything to your perception of the dynamic properties. Two different objects with the exact same zero-, first- and second-order moment, when acted upon by the same forces (you could have a different force on each and every tiny bit you've divided the object into if you want) will act exactly the same. So neglecting the second order moment amounts to discarding a whole part of what you could measure of weapon dynamics. And measuring it is not opening a Pandora's box of plenty of other measures because up to second order is all you need for dynamics.

The drawing I posted earlier was just an illustration of how pivot points move when you move your point of reference, not really an illustration of the physical theory behind. Note that it's not just levers, the inertia is represented, it's on the vertical axis... Pivot points are really the result of an interaction between geometry (your point of reference), on the horizontal axis and inertia on the vertical axis.

Blade harmonics don't lend themselves to such a simple analysis (well, maybe dynamics seem simple to me partly because I'm becoming a reresearcher in applied mathematics and I've been thinking about that for something like 3 years ). The nodes of vibration depend on mass distribution, cross section, material properties... That is, I think, what makes their relation to mass distribution (and its modifications) non obvious. But Angus can speak of that a lot better than I ever would

So of course there are plenty of ways to get the three moments right. The key problem for sword making is then to get them right while having a solid blade with good profile, good blade harmonics, beautiful hilt but solid, and so on. But it's art and not science at this point. However, if you have one of the moments wrong by an amount too great, it probably won't feel like an original no matter the art (though it could feel right, it will certainly not feel the same). I'm fairly certain that good sword makers have their ways, at least intuitive, to get the dynamics right even without measuring. But measuring, in my opinion, can only help...

As far as getting anything to feel exactly like an antique, its nearly impossible to get two swords of the same model, even using CNC tech for the roughing profile and contour, to be "exactly" the same. Though frankly, it depends on a person's abililty to "feel" things when things are close enough......

That hand work thing, little things, like edges being just a hair off one to the other, a fuller a bit different, the tang not perfectly the same, the handle length, diameter, crossection a bit different, the wrap making its individual "feel" noticeable.......

Something will make itself felt to someone that has the sensitivity for it.........

You can get close, "real close", but for the real sensitive, there will always be something just a wee bit different........

I like what your doing, Vincent....... now all you need to do is come up with a formula that factors in the difference that blade width adds to an equation, the tapers, how the grip and hand interact, etc......*g*swords are fun

As far as getting anything to feel exactly like an antique, its nearly impossible to get two swords of the same model, even using CNC tech for the roughing profile and contour, to be "exactly" the same. Though frankly, it depends on a person's abililty to "feel" things when things are close enough......

That hand work thing, little things, like edges being just a hair off one to the other, a fuller a bit different, the tang not perfectly the same, the handle length, diameter, crossection a bit different, the wrap making its individual "feel" noticeable.......

Well yes, since we are talking of hand-made objects, that's what I would expect indeed. I think we should try, ideally, to reproduce antiques to the point they don't really stand out in a set of reproductions of the same model. That is, you make several reproductions, with the same process, they are different. But if the difference in feel between the antique and any of those reproductions is about the same as the difference between two reproductions, I'd assume you are as close as you'll ever get

Of course the last paragraph is not necessarily practical because it assumes that you have an antique in a really good state as well... and that you are making several reproductions. But you get the idea.

Angus Trim wrote:

I like what your doing, Vincent....... now all you need to do is come up with a formula that factors in the difference that blade width adds to an equation, the tapers, how the grip and hand interact, etc......*g*

But but but yes, but I already have Well it satisfies me, for the time being at least, and I'm not demanding that everybody uses it, it's just that I find it pleasant and I want to share It's what I exposed in my first post in this thread, in fact...

Let's get more specific:

* blade width: It changes every little mass m in my previous post. So yes, the inertia and COG would change, changing pivot points -- check
* tapers: it's exactly the same idea. When you taper a blade, you remove mass from each little segment of the blade, thus modifying all the mass distribution, then changing cog and pivot points -- check

And what you mentioned earlier:

* fullers: well it's still the same idea, you change the little masses of the segments, and so pivot points change -- check
* tang not the same: changing the masses again and maybe even adding some other (if you change the length) -- check
* handle length: for one it changes the masses (adding or removing them, depending on if you shorten it or lengthen it). And it changes the reference points you have to consider. So, well, there is a fair amount of chance that everything will have changed, inertia, center of gravity, kind of tip control, tracking in cut, etc. -- check

OK so I'm having fun putting everything in a check list (hence the swarm of smileys) but really it's all the same. The fact is that every operation you mentioned acts on the masses, and so will change all the dynamic properties, and not just one. One nice thing is that since the equations giving pivot points, center of gravity, etc. are relatively simple, you can predict the effect of the modification of the mass at a given position. For example, if I add weight to the pommel of a sword, getting it's center of gravity 1cm closer, I can predict where the pivot point of the cross will end up. Doing the same with blade harmonics borders the impossible as far as I understand the theory behind them...

Also, many seem to think that pivot points are something that is relatively insensitive to mass modifications on the blade, and that you just act on the pommel weight to adjust pivot points (could come from George Turner's article since he insisted on that quite a bit, too much in my opinion). It's quite the opposite... modification of the mass over the whole blade has a far greater impact. I think it's something Craig Reynolds has already mentioned in a thread I came across. You don't balance a sword just by acting on the pommel...

But back to the "check-list":

* hand-grip interaction: ah there you have me I'd be hard-pressed to find something about that since it's linked to the hand... I'd think that if the grip has the same geometry and materials, that part is the same for two different weapons.

So yes, my approach fails when the human comes into play. But I feel that any quantitative approach will. The human being, even just one hand, is something way too complicated. Surely an ergonomist would have plenty to say about that... In a way, you could say that I take a really rough account of the human factor in the way I choose my ratios and length. But not something as precise as a hand model, I'm afraid...

Again, if you feel you can get this sort of grasp with blade harmonics, it's fine with me, if it's a good sword in the end it doesn't really matter. I've said before I was more seeing all this with a user perspective, it's just my way to appreciate weapons... Blade harmonics are maybe another, I'm less at ease with them, that's all.

I hope I'm not bothering anyone with all those posts, be sure to warn me if it's the case, I tend to be a little... talkative about all that

I want more illustrations and examples and then I'm going to cut and paste this entire thread, print it out and keep it as a primer on sword/blade dynamics and harmonics/etc... (I'm quite serious here: this is some of the *most* useful sword related information I've come across online - even if I *don't* understand it all yet...)

Something tells me there won't be many books like THIS on Amazon either...:-)

John.

PS I wonder if anyone *has* ever attempted to write a book actually covering the sort of concepts/principles/science related to swords like you chaps have been discussing? I have *many* different sword books but NONE of them cover this incredibly interesting (and IMPORTANT) area... The more I think about it (in light of this discussion), the sword books I have are like car books with lots of pictures and info but almost NO discussion on how the vehicle actually works/performs/functions...

I want more illustrations and examples and then I'm going to cut and paste this entire thread, print it out and keep it as a primer on sword/blade dynamics and harmonics/etc... (I'm quite serious here: this is some of the *most* useful sword related information I've come across online - even if I *don't* understand it all yet...)

Something tells me there won't be many books like THIS on Amazon either...:-)

John.

John,
There's really no need to cut, paste and print this thread. Since it's a spotlight topic, it's accessible from the Spotlight Topic Page. You can also click "Add to favorites" at the top of each page of a thread to add the thread to your favorites page, accessible by clicking "Favorites" between "Profile" and the PM Inbox button. If you want to use up your paper, we can't stop you, but there are plenty of ways to keep this info handy that don't involve all that work.

I hope I'm not bothering anyone with all those posts, be sure to warn me if it's the case, I tend to be a little... talkative about all that

Regards

Mr Le Chevalier
Not bothering me, I find it fascinating. Concentrating on the masses covers a lot (maybe enough?) in terms of sword behaviour, but given that they (until now at least) tend not to be used in a vacuum, would there be any way of incorporating aerodynamics in your analysis, such that volumes and shapes, as well as mass distribution, were taken into account?
Regards
Geoff

Concentrating on the masses covers a lot (maybe enough?) in terms of sword behaviour, but given that they (until now at least) tend not to be used in a vacuum, would there be any way of incorporating aerodynamics in your analysis, such that volumes and shapes, as well as mass distribution, were taken into account?

Hmmm... personally, I'd think it would be too much. Aerodynamics are really a complex subject, they depend not only on the shape of the weapon but also on its motion.

In fact there are two cases I can distinguish. For thrusting weapons, I don't see aerodynamics as having a great influence, because they move too slowly to generate a significant drag. Air is not that dense...

For a cutting weapon, one should take into account that the fastest motions are made in the edge plane, during cutting. So yes, obviously there could be a significant drag, maybe even a bit of portance. On the other hand, the profile of the sword, the shape of the edge, are built with cutting in mind. Thus, the edge is by itself already quite aerodynamic, since it's designed to cut through flesh which is much more resistant than air...

I believe, though I'm unable to back that up by any proper evidence, that historically the compromise was more between mass distribution and edge profile with cutting in mind, and that aerodynamics were considered as a side effect.

The only significant effect I've felt of aerodynamics was with wooden weapons, since they have a bigger cross-section. And even then, I feel it only when swinging a staff at maximum speed, while holding it close to its butt. I find it quite low when compared to the effort I have to make to get the weapon to move, or stop. Fighting weapons are generally dense enough to make neglecting aerodynamics reasonable, I believe.

John,

I'll try to make a post relating what I've been able to observe on the limited set of weapons I have had access to, for the sake of example. Maybe other will be able to experiment and will report back as well.

But remember that to get a grasp of the concepts, you can experiment with almost everything. I mean, a simple wooden stick can provide you with valuable insight about pivot points. You can move your grip to feel how your perception of the weapon change, you can mark a few specific points (center of gravity, pivot points associated to each end, and so on)... You could even try to taper your stick to see how the properties change, add a bit of metal wire to simulate a pommel, etc. It's way simpler to make experiments about pivot points than about harmonic balance, because you don't even need a proper metal blade

As far as books are concerned, maybe the problem is that the average sword collector is not really concerned by dynamics for the time being. It's mainly important for those who use the sword, and it takes some familiarity with physics and maths to understand them properly. Moreover, as has been pointed out in the beginning, the matter has turned somewhat political, and this could have scared authors... The human being has this amazing gift to turn everything, even physics, into politics, you see

Hi Mr Le Chevalier
Thanks for the response. I've tried looking up portance and I can only find it in french (and my french is about 40 years rusty). Would it be expressing an equivalent idea to that which I'd call 'lift'?
Geoff

Hi Mr Le Chevalier
Thanks for the response. I've tried looking up portance and I can only find it in french (and my french is about 40 years rusty). Would it be expressing an equivalent idea to that which I'd call 'lift'?
Geoff

Please, no need to say sorry, I like learning new words. I recall having a discussion with Mr Trim about possible effects of lift when cutting, but I think it was in 'another place' which I no longer frequent and I can't now remember whether he said he'd seen/felt evidence of such effects or not. As you said before, effects were probably small in any case.
Geoff

Hi Mr Le Chevalier
Thanks for the response. I've tried looking up portance and I can only find it in french (and my french is about 40 years rusty). Would it be expressing an equivalent idea to that which I'd call 'lift'?
Geoff

Short answer: YES, lift as in the vertical forces that keep an aircraft in the air. ( From my Larousse French dictionary. )You can easily give up your freedom. You have to fight hard to get it back!

Please, no need to say sorry, I like learning new words. I recall having a discussion with Mr Trim about possible effects of lift when cutting, but I think it was in 'another place' which I no longer frequent and I can't now remember whether he said he'd seen/felt evidence of such effects or not. As you said before, effects were probably small in any case.
Geoff

Hi Geoff

{Mr. Trim? How about just Gus?}

I recall that, and at the time, all of the stills we had of a blade "in the cut" before contact, had the blade lifting a bit before contact.... if the blade flexed before contact at all {depends on rigidity etc}......

Since then there have been a couple of stills taken where the blade flexes a bit downward before contact......I can't explain it, don't really know what's going on, though it wouldn't surprise me what is being seen is the effects of the blade being slightly "offline" during the cutting motion. However, I don't know.......swords are fun

I recall that, and at the time, all of the stills we had of a blade "in the cut" before contact, had the blade lifting a bit before contact.... if the blade flexed before contact at all {depends on rigidity etc}......

Since then there have been a couple of stills taken where the blade flexes a bit downward before contact......I can't explain it, don't really know what's going on, though it wouldn't surprise me what is being seen is the effects of the blade being slightly "offline" during the cutting motion. However, I don't know.......

OK, thanks Gus, and thanks for your memory too. Offline, as you say, would make sense, leading edge up would give lift up and vice versa (if you can call it lift when it acts downwards).
regards
Geoff

So here, pendulum = the distance between the aft pivot point and the point of the grip farthest from the center of balance. It's in centimeters. The idea being that while the sword is swinged (in cutting for example), it's akin to a pendulum with this length... So the smaller the length, the faster the tracking of the weapon would be. As I said before you're not necessarily aiming at a very short length, it should be in proportion with the amplitude of your motions.

Blade mass, tip control and static feel are defined as I explained in my first post in this thread. They are ratios of lengths so they have no units.

Some background about the weapons:

* the foil was the training weapon of one of my ancestors... But I have seen modern foils with much the same properties as far as pivot points and dynamic balance are concerned.
* the Milanese Rapier is the one from Arms&Armor (thanks again Craig )
* the Type XI I bought from Albion when they were selling swords by Angus Trim (my first real sword, so thanks as well Gus )
* the measurements of the cavalry saber were taken from the full PDF version of George Turner's article (I don't remember where I got it from) so I can't be absolutely sure they are exact
* the axe is a cheap low quality wall-hanger... I include it here because it has the most extreme balance I've ever seen (i.e. all the weight is in the head because the wood is incredibly light)
* the boken (wooden japanese saber) is a rather classic one made out of white oak
* Iaito 1 and 2 are two examples of how the balance can vary among weapons seemingly of the same type. Iaito 2 is significantly better finished, while iaito is I belive of lower quality. I included stats for iaito 2 when used one-handed, to illustrate how they change. For those who may not be so familiar with japanese martial arts, a iaito is a training sword replacing the katana for practice. It's less sharp, generally lighter as well. I'm afraid I don't have a katana at hand

Now some comments of the results:

* The length of the equivalent pendulum seems rather uniform. The foil, the rapier and the type XI are the fastest for realignment. The axe is the slowest, which makes sense since you need bigger arcs to put energy in it anyway... But the difference is not so big.
* Differences in blade heaviness are more significant... The axe being clearly the heaviest. Note the big difference between the iaitos. I can assure you that it's coherent with what everybody who has ever handled those two weapons said.
* For tip control, remember that 1 means that the pivot point associated to the cross is at the tip. For the foil this forward pivot point is actually beyond the tip... But I have found out that I don't ordinarily hold it with the index flushed to the guard, but instead at the point that gives me a pivot at the tip. I haven't modified the results according to that, but it's probably something I should do. Pure cutting weapons (type XI, cavalry saber) tend to sacrifice tip control to favour blade mass. Note once again the difference between the iaitos... I can't say for sure that iaito 2 has it right though, but I prefer it anyway The axe is not bad because you have obviously a good feeling of where is the "tip" (it has a spike at the end and almost all the weight is very close to that) but because of the mass you'd have trouble fencing with it
* The static feel gives coherent results. The extreme value for the cavalry saber is the result of a very short handle and of a center of gravity quite far out.

There are other things you could say about those weapons, but I wanted to share just that, to show what you can pull out of the simple ratios I defined. Hence I have not included length, hilt size, etc. Not that I'm perfectly happy with the ratios; for example, I'd like to include an effect on the tip control when you grab the weapon one handed. I've got plenty of ideas for that (some originating from the discussion here) but they are not really ready yet...

And a last note about harmonic balance: the node of vibration of my type XI is quite exactly the forward pivot point... I'm fairly sure it's not a coincidence. It's not true for the milanese rapier, but it still seems that the two nodes are associated, i.e. the node on the blade is the pivot point associated to the node on the handle. Possibly it's something that comes from the "no shock" effect everyone is looking for at harmonic nodes. I think there is something to dig out here as well, but I don't have enough "harmonic" weapons to attest it. So either I buy more weapons or someone else tries... or both

And a last note about harmonic balance: the node of vibration of my type XI is quite exactly the forward pivot point... I'm fairly sure it's not a coincidence. It's not true for the milanese rapier, but it still seems that the two nodes are associated, i.e. the node on the blade is the pivot point associated to the node on the handle. Possibly it's something that comes from the "no shock" effect everyone is looking for at harmonic nodes. I think there is something to dig out here as well, but I don't have enough "harmonic" weapons to attest it. So either I buy more weapons or someone else tries... or both

Regards

No, its no coincidence, nor accident.......

I want to encourage you to continue this Vincent....... I think you're going to be doing both the sword enthusiast, and sword making crowd some good.

Once upon a time, when swordmakers wrote about their art and science, they were quite sincere, and helpful. Everybody was elated to find others of similar interest, and everyone had something to relate, and this new medium helped with the communication.

Then several dynamics came together during an 18 month period, and an awful lot of what has been written since has been somewhat tainted. Either by politics, ego, paranoia, or just plain bs......... Its a shame.......And until about a year ago, I was as guilty as many.

Still, for someone interested in the "truth", there's still a few nuggets in some of the stuff written in the last four years. As much politics as there is in George Turner's article, its still the first article that took things from the subjective "follows the tip naturally", or "tracks naturally", and added a little science to it. Its time, and past time to begin again researching and talking honestly about these traits........

And really, at this stage of the game, it needs someone that has some "investment" in this. If you're somewhat vested in these things, your credibility is going to be questioned by some, even if it can't be done publicly because of fear of backlash.........

If just studying the things written in the last four years, well, take a bit of some of it with a grain of salt. There's been a few eggs and or booby traps left, that wouldn't have been if "we" weren't a bit paranoid, or political during that period.

I'd like to encourage you, and help, but frankly, I don't know how much help I can really offer over the next year. Don't trust any of what you've read over the last four years without verifying it yourself..........swords are fun

I want to encourage you to continue this Vincent....... I think you're going to be doing both the sword enthusiast, and sword making crowd some good.

That's about the best I can hope for... But when I started all this "research" I was not aiming quite so high Selfish as it may sound, I was working for my understanding alone. It's only recently that I felt some urge to share.

Angus Trim wrote:

Still, for someone interested in the "truth", there's still a few nuggets in some of the stuff written in the last four years. As much politics as there is in George Turner's article, its still the first article that took things from the subjective "follows the tip naturally", or "tracks naturally", and added a little science to it. Its time, and past time to begin again researching and talking honestly about these traits........

That's quite exactly what I thought when I first read this article. The politics were unknown to me at the time, so I was looking at that with something of a "neutral eye". Also, as english is not my first language, I did not perceive some jabs or aggressiveness, so I saw only the informative content first...

Angus Trim wrote:

And really, at this stage of the game, it needs someone that has some "investment" in this. If you're somewhat vested in these things, your credibility is going to be questioned by some, even if it can't be done publicly because of fear of backlash.........

Well, everyone is entitled to his own opinion. Not being a swordsmith, I'll only ever propose a way of looking at the swords, and I will not be trying to somehow "implement" my views in steel. If there are other ways of explaining, it's not my goal to attack them. What would I win anyway?

I'm aware that I have a rather low credibility over all this, being neither a recognized martial artist nor a famous swordsmith. On the other hand, being relatively free of political or commercial prejudice is something I enjoy

Angus Trim wrote:

I'd like to encourage you, and help, but frankly, I don't know how much help I can really offer over the next year. Don't trust any of what you've read over the last four years without verifying it yourself..........

Oh, but this kind of discussion is great help already! In fact there is only one thing I really miss: measurements on a wider set of weapons. But obviously it's not easy to get measurements for a theory that is not "mainstream", so...

As for trust, I already have difficulties trusting what I write myself at times I can tell you I have a pile of my own writings from the past 3 years, and that there is a good part of those that I now consider worthless (but I keep it for my edification ). I have already tried many paths and reached some dead-ends...

In fact I now realize that I haven't been reading much about this. Maybe a few forum threads, some articles (but there are few that go into physics)... Apparently the kind of "holly wars" there's been discouraged quite a few people to even think about it, which is a bit sad. Still, reviews were (and are) really useful to me, because they highlight interesting properties, even without numbers, properties that I can then try to translate into physics.

Well, maybe this research is like trying to get to the end of the rainbow... I guess someone has to try it anyway

This thread inspired me to add something more to the usual measurements I do with my swords. It took me some time, so am late in the thread, but perhaps still helpful.
I keep all my measurements in EXCEL sheets, which easily enables doing graphic representations. You can see in the two attached figures the measured profile taper of my Albion BARON and my AT 1555 sword (all figures are metric).

Usually I measure in addition CoG, CoP and the guard pivot. Inspired by Vincent's simple formula on how to deduct any pivot from a given pair, I experimented with measuring and tweaking the results to fulfill the formula. What you can see as the pink line in the graphs are both extreme pivot points (from pommel and guard), measured and deducted by the formula - so as close to the "truth" I can get. On the pink connecting line are all theoretical possible pivot points possible from the hilt. For illustration I have also marked the measured "Center of Percussion".

My first interpretation of the figures:
- CoP for both swords is within the pivot point line. I don't know if this is good or bad, or typical. Have to measure more swords to find out.
- The Baron has the pivot points surprisingly far away from the point. If the pink line is the zone for optimal cutting, it's as far behind as two thirds to half of the blade. But as an Oakeshott XIIIa the Baron is a great cutting war sword - no real surprise on that.
- The AT 1555 has its pivot points closer to the tip, like expected from a later XIIIa sword. This sword is more suited to elaborate techniques in bind, like winden or duplieren, which would happen around the guard pivot point.
So for a practitioner it's quite interesting to know about the location of the pivot points on his sword in order to use them properly. I might mark the "pink zone" with two rings of coloured tape on my training sword and try to wind within this zone

I will repeat these measurements for my Albion Landgraf, which is a very pointy XII, and expect the pivot points to move even further to the point.
In this context I have a question to Vincent: is it possible that the guard pivot may be outside the blade, somewhere in front of the point? The formula allows it. What kind of dynamics would such a sword have?

This thread inspired me to add something more to the usual measurements I do with my swords. It took me some time, so am late in the thread, but perhaps still helpful.

There's no need to worry about being late, after all we're studying things from several hundred years ago here, so I guess we're not really in a hurry

Ralph Rudolph wrote:

Usually I measure in addition CoG, CoP and the guard pivot. Inspired by Vincent's simple formula on how to deduct any pivot from a given pair, I experimented with measuring and tweaking the results to fulfill the formula.

Yes, the formula is helpful because it allows to control the measurements. It's quite necessary since the "waggle test" is not absolutely accurate (it becomes exact when the back and forth motion has a high frequency), and not so easy to perform...

Ralph Rudolph wrote:

My first interpretation of the figures:
- CoP for both swords is within the pivot point line. I don't know if this is good or bad, or typical. Have to measure more swords to find out.

Apparently this seems to be the case on most swords, but I'm not completely sure of what it means. As I said I'm not advanced on the link between harmonics (COP) and dynamics (pivot points) so I would not judge a sword based on that...

Ralph Rudolph wrote:

- The Baron has the pivot points surprisingly far away from the point. If the pink line is the zone for optimal cutting, it's as far behind as two thirds to half of the blade. But as an Oakeshott XIIIa the Baron is a great cutting war sword - no real surprise on that.

The pink line is not necessarily the best part to cut with. Impacts involve more than just the sword, you have to at least take into account its motion and the mass of the target (that would be the crudest model). I've done a few formal calculations with that, and the area where the most energy is used for the cut (i.e. not for moving the target) moves to the tip when the target is lighter. Plus if you want to avoid vibrations you have to take the COP into account. Oh, and the blade profile, of course So in the end you cannot really find the exact good spot for cutting, rather you adapt your cut to the circumstances. If during a fight you can make a cut that will dissipate 10% less energy but will still kill your opponent and would make you safer because you have 20cm more of reach, I think it's a wise thing to do...

The pink line is only the right place to cut at a target with infinite mass, hacking down a tree would be an example. But swords are not meant to do that

Anyway in terms of placement of pivot point your Baron is quite close to my type XI, i.e. something adapted to be quick and powerful in cutting motions while sacrificing a bit of tip control. Moving the forward pivot point while retaining blade mass would result in a slower tracking in cut...

Ralph Rudolph wrote:

- The AT 1555 has its pivot points closer to the tip, like expected from a later XIIIa sword. This sword is more suited to elaborate techniques in bind, like winden or duplieren, which would happen around the guard pivot point.

I don't really know since I don't have a significant experience with longswords, but from what I can see about the AT1555 your conclusion sound right.

If I may dare commenting a bit about this, I'd like to correlate the position of the pivots with what can be read in the review here. Seeing your figures, I was thinking that the pivot point of the pommel might be a bit further away than what I ordinarily like (so it's typically something personal and linked to one's style), something like 75cm away from the pommel if I'm not mistaken? This tends to slow the tracking of the blade a bit. And indeed in the review:

Caleb Hallgren wrote:

It doesn't accelerate in the effortless manner of a smaller, lighter blade. It takes effort to get it moving into a swing.

Which I take to mean that you have to put a good amount of torque with your hands, since pendular behaviour is not enough to sort of "bring the sword into the cut"... On the other hand, indeed the forward pivot point is close to the tip, which concurs with both your observations and the reviewer's.

All this shouldn't be taken as a criticism of the swords of course, but rather as a try to link dynamic properties in words to dynamic properties in measures.

Ralph Rudolph wrote:

So for a practitioner it's quite interesting to know about the location of the pivot points on his sword in order to use them properly. I might mark the "pink zone" with two rings of coloured tape on my training sword and try to wind within this zone

Glad you like them

Ralph Rudolph wrote:

I will repeat these measurements for my Albion Landgraf, which is a very pointy XII, and expect the pivot points to move even further to the point. In this context I have a question to Vincent: is it possible that the guard pivot may be outside the blade, somewhere in front of the point? The formula allows it. What kind of dynamics would such a sword have?

It's entirely possible, though it's not something that I think would happen with a sword meant for cutting. I have seen a wall hanger that had this behaviour once. In short, if you have a blade and you add a pommel too big on it, it will eventually move the cross's pivot point outside the blade. As far as I understand the effects of pivot points, it's not something you wish to do in general. Indeed it will:

* lower the tip control, since what you feel is not on the blade but beyond. In fact you're feeling a mass that is purely virtual and gives you no indication of the blade or tip position
* lower the blade mass. To bring the pivot point beyond the tip you have to bring the center of balance closer to the guard, thus diminishing blade mass even more. So not only you feel a mass that is not on your sword, but it's a small mass.
* it will also give a funny feeling for tracking in cut. In fact, when you add mass to the pommel, its pivot point does not move, so the pendular behaviour is still the same. However, you will feel like you'd want to grasp beyond the pommel on such a sword, because you can feel in your hand that gripping there would lower significantly the pendulum's length. In general, on swords meant for cutting, or quick rotating motions, I found that the pendulum length at the pommel is quite close to the minimum you can have on the sword. Moving this minimum beyond the pommel could possibly feel awkward.

You can get an idea of how it feels if you like, by gripping a stick very close to the center of gravity. Or you could add a big removable mass to the pommel on one of your swords... You'll see what I mean, I think.

In fact it's one of the problems I had with the article by George Turner, because he emphasized quite a lot that the pivot point of the cross should be at the tip no matter what. But trying to balance my type XI like this does not feel right (and would require a really big pommel).

Remember also that pivot points don't necessarily move together. It's possible that on your Landgraf, the forward pivot point gets closer to the tip, while the pommel's pivot point stays around the middle of the blade (I'm not saying that it's what should happen either, but it's possible)... There are really a lot of possibilities, depending on how the maker played with the pommel, tapers, proportions... That's the beauty of the thing

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